[kraitis]

>What then is a mathematical truth

In the West, Aristotle put it as follows: "To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true"

Some 2 millennia later, Tarski, a Polish logician, more or less formalised just that. This result, among other things, spawned a brand new branch in mathematics: Model Theory. More on Tarski’s notion of truth: https://plato.stanford.edu/entries/tarski-truth/. A few decades later some analytic philosophers like Davidson drew on Tarski’s work and applied it to natural language, too. This resulted in this: https://en.wikipedia.org/wiki/Truth-conditional_semantics. But notwithstanding Tarski’s work, there’s still significant controversy surrounding both “truth in natural language” and the logico-mathematical truth predicate in philosophical circles. Here’s an article that covers axiomatic theories of truth in general: https://plato.stanford.edu/entries/truth-axiomatic/.

[asfasgasg]

The clock problem is, as it seems most philosophical problems I seem to encounter, one of definitions. It's a game with words. It doesn't change the underlying facts. You had a good reason to believe proposition X, and X happened to be true, but your reason to believe X was not causally linked to X's fact-ness. Whether you want to call that circumstance "knowledge" or use some other symbol to describe it does not change the underlying fundamentals at all. And so all the millions of hours of thought that have been spent on this problem have been wasted.

[sullyj3]

This mistake of reifying of non-fundamental concepts and then thinking about them without reference to their component parts is an epidemic in philosophy, and it always has been.

[ahussain]

The problem with this dismissal is that "knowledge" is not just a word, it does in fact refer to something solid and concrete (insofar as most of us intuitively believe there is a difference between genuine knowledge and just belief).

In the real world it is impossible to find human experiences that are "causally linked" to facts in the world, and so the implication of the argument is that EVERY experience you have ever had is possibly like looking at the broken clock.

And yet, most of us would believe that there is a difference between looking at a broken clock that says noon, versus a working clock that says noon. It would be nice to have a rigorous way to distinguish between the two cases - solving that problem might teach us something about the world.

[asfasgasg]

>The problem with this dismissal is that "knowledge" is not just a word

"Knowledge" is just a word. It references many different concepts.

> In the real world it is impossible to find human experiences that are "causally linked" to facts in the world

Either you've misunderstood what causal linkage is, or else you are some odd brand of solipsist, but either way, this is incorrect. Causal linkage just means that that event participated in causing this event. The sun being in the sky is causally linked to me believing it's day time, for example.

> And yet, most of us would believe that there is a difference between looking at a broken clock that says noon, versus a working clock that says noon.

Of course there is. In one case, your belief is causally linked to fact. In the other case, it isn't, but still happens to be correct.

[ahussain]

> Causal linkage just means that that event participated in causing this event. The sun being in the sky is causally linked to me believing it's day time, for example.

Great example! In Ptolemy's time "the sun being in the sky" would have meant that the sun was in a particular phase in its orbit around the Earth. Now we understand that the sun is not actually "in the sky" but it is a hundred million kilometres away. Our understanding of what it means for the sun to be "in the sky" will likely undergo several revolutions in the next 100,000 years.

Second, the actual facts are not causally linked to your belief. Your perception that the sun is in the sky is causally linked to your belief that it is daytime. If I am a schizophrenic and I hallucinate that the sun is in the sky even though it is night time then do I "know" that it is daytime?

All of this probably sounds overly pedantic but teasing apart the details is exactly what we're trying to do here :)

[hshehehjdjdjd]

(Same person, different account.)

> Our understanding of what it means for the sun to be "in the sky" will likely undergo several revolutions in the next 100,000 years.

I wouldn’t bet on it.

> Your perception that the sun is in the sky is causally linked to your belief that it is daytime.

My perception is cause by electrical impulses from my eyes, which are caused by photons hitting those receptors. The photons themselves are caused by the sun, and their incoming vector is caused by its position relative to me. There is a causal chain, thus, causal linkage.

> If I am a schizophrenic and I hallucinate that the sun is in the sky even though it is night time then do I "know" that it is daytime?

Depends on what you mean by know. Your perceptions are not causally linked to a true belief, if that is what you are asking.

[Brotkrumen]

Imagine you are designing a software system. One use case requires you to model a fact as best as you can, so you write a fact-class for it. Your software system runs fine, but you notice the class doesn't accurately model the fact in some other use cases. You now know the class is insufficiently accurate. Do you still trust the result of your software?

Replace software with language, class with concept we use to refer to facts and you have to claim that any further thought into the design of your class is wasted, because you hold that to be the case for concepts, language and reality.

[asfasgasg]

If all philosophers are talking about is how underspecified words are, that is fine, but there's little value in it. Language is not designed. So a word is underspecified. Nobody can fix it.

But I was under the impression that philosophers thought themselves more than mere dictionary debaters. Whenever I hear about this problem, my impression is that at least non-zero of them think there is a problem with the actual concept of knowledge, not merely the word.

[LoSboccacc]

we're just into another 'what's truth' cycle. next will be 'is truth communicable' then 'is truth subjective'